changes in the force–velocity relationship of fatigued muscle: implications for power production...

Download Changes in the force–velocity relationship of fatigued muscle: implications for power production and possible causes

If you can't read please download the document

Upload: david-a-jones

Post on 02-Aug-2016

218 views

Category:

Documents


1 download

TRANSCRIPT

  • J Physiol 588.16 (2010) pp 29772986 2977

    TOP ICAL REVIEW

    Changes in the forcevelocity relationship of fatiguedmuscle: implications for power production and possiblecauses

    David A. Jones

    Institute for Biomedical Research into Human Movement and Health, ManchesterMetropolitan University, Manchester M5 1GD, UK and School ofSport and Exercise Sciences, University of Birmingham, Birmingham B15 2TT, UK

    Slowing of the contractile properties of skeletal muscle is one of the characteristic features offatigue. First studied as a slowing of relaxation from an isometric contraction, it has becomeapparent that this slowing is indicative of functional changes in muscle responsible for a majorloss of power with all its functional repercussions. There are three factors contributing to theloss of power inmammalianmuscle at physiological temperatures, a decrease in isometric force,which mainly indicates a reduction in the number of active cross bridges, a slowing of themaximum velocity of unloaded shortening and an increased curvature of the forcevelocityrelationship. This latter change is a major cause of loss of power but is poorly understood. It isprobably associated with an increase in the proportion of cross bridges in the low force state butthere are no clear candidates for the metabolic changes that are responsible for this shift in crossbridge states. The possibility is discussed that the reduction in activating calcium that occurswith metabolically depleted muscle, alters the distribution of cross bridge states, affecting bothshortening velocity and curvature.

    (Received 1 April 2010; accepted after revision 11 June 2010; first published online 14 June 2010)Corresponding author D. A. Jones: School of Sport and Exercise Sciences, University of Birmingham, BirminghamB15 2TT, UK. Email: [email protected]

    Muscle function in the body depends on a long chainof command starting from motivation, and even withinthe muscle fibres there are many steps between electricalactivity in the surface and T tubular membranes andthe molecular interaction of actin and myosin (Edwards,1981). It would be wasteful of energy and resources tohave certain parts of the chain over-engineered so thedifferent links in the chain are all likely to fail at aboutthe same time when the system is stressed. It is unlikely,therefore, that there is any one site or mechanism offatigue that applies to every situation. Thus the preciselink which fails will vary depending on a range offactors including the type of activity, the type of muscleand the temperature, and when discussing fatigue it isimportant to specify the preparation and conditions under

    This review was presented at The Journal of Physiology Symposium onModern views on muscle physiology and pathophysiology: Progress alongthe trail blazed by Professor Richard HT Edwards, which took place at theJoint Meeting of the Scandinavian and German Physiological Societies,Copenhagen, Denmark, 27 March 2010. It was commissioned by theEditorial Board and reflects the views of the author.

    which the muscle is working. This short review willbe concerned with mammalian, mainly human, muscle,undertaking metabolically demanding exercise at physio-logical temperatures of around 37C. There have been anumber of recent detailed reviews ofmuscle fatiguemainly

    David Jones graduated in MedicalBiochemistry from the University ofBirmingham and completed his PhDin Neurochemistry at the Institute ofPsychiatry in London. With a family andhouse to support he changed fields andwent to work at the Royal PostgraduateMedical School on basic muscle physio-logy and studies of patients with muscleproblems. He continued these interests atUCL and in 1993 returned to Birmingham as Professor of Sportand Exercise Sciences; he is currently Emeritus Professor of MusclePhysiology at Manchester Metropolitan University. He has wideinterests in muscle and exercise physiology but his abiding concernhas been the changes in contractile function that occur with acutefatigue.

    C 2010 The Author. Journal compilation C 2010 The Physiological Society DOI: 10.1113/jphysiol.2010.190934

  • 2978 D. A. Jones J Physiol 588.16

    Figure 1. Relaxation rate, sampled during and after contraction at 50% MVC in one subjectThe short breaks for testing t1/2 (the half-time of the relaxation phase) as fatigue progresses and short (3 s) testcontractions during recovery are indicated below. Inset: two records of relaxation to show prolongation withfatigue (from Edwards et al. 1972).

    from Allen, Lannergren, Westerblad and colleagues (e.g.Allen et al. 2008) which have concentrated largely on theprocesses of excitationcontraction coupling and loss offorce. Consequently the present review will take a slightlydifferent angle, concentrating on the slowing of contractileproperties.

    In 1971 Richard Edwards was working in theRespiratory Unit at Hammersmith Hospital after asabbatical in Scandinaviawherehehad acquired theneedlebiopsy technique that he was to introduce into the UK. Hehad a grant from the Muscular Dystrophy Group of GreatBritain to set up a muscle testing laboratory in which hewas greatly helped by David (D.K.) Hill who was head oftheMedical Physics Department at the Royal PostgraduateMedical School. Although theMDGB grant was to look atmuscle disease, Richard had yet to establish himself as anauthority on muscle disease and patients were slow to bereferred in the first year or so. During that time, at David

    Figure 2. Brief tetanic contractions of the human first dorsalinterosseous in the fresh state and after a fatiguing 45 sischaemic voluntary contractionHorizontal bar indicates the duration of stimulation at 50 Hz (fromCady et al. 1989).

    Hills suggestion, Richard began a study of muscle fatiguein healthy subjects and, in particular, the characteristicslowing of relaxation which at that time had hardly beendocumented, let alone explained.

    Changes in contractile properties with fatigue

    The slowing of relaxation is illustrated in Fig. 1 showingthe effect of fatigue in one subject (R.H.T.E.) during aprolonged voluntary contraction of the quadriceps, inter-rupted at intervals to measure the rate of relaxation. EMGactivity was recorded to demonstrate that the relaxationphase was electrically silent and that the slowing was afunction of changes in the contractile apparatus of themuscle rather than a slow decline in voluntary activation.The observation has since been repeated many times ona wide range of human muscles, generally using electricalstimulation which avoids any suspicion of continuedvoluntary effort, with animal muscle both in situ andin vitro and with all fibre types, including the slow soleusmuscle (Edwards et al. 1975). Typical of these results arethe brief tetani shown in Fig. 2 (Cady et al. 1989) wherethe isometric force is reduced and the relaxation phase isprolonged in the fatigued muscle. In isolated single fibrepreparations (Fig. 3; Westerblad & Allen, 1993), the lossof force occurs in two phases: a relatively small initial lossthat is associatedwith a small increase in intracellularCa2+

    and is probably due to an inhibition of force production byinorganic phosphate (Pi), and then a second more rapidloss of force that is accompanied by a reduction in calciumrelease. The same combinationof events is almost certainlyresponsible for the loss of isometric force in Fig. 2 although

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • J Physiol 588.16 Changes in the forcevelocity relationship of muscle with fatigue 2979

    howmuch of the force loss is due to a direct effect of Pi oncross bridge function is not known; see below.

    The cause of the decrease in calcium release is stilluncertain but interest focuses on the possibility that Pienters the sarcoplasmic reticulum where it binds withthe stored calcium thus reducing the quantity availablefor release. A possible slow diffusion of Pi into the SRor regulation by ATP might explain why there is a poortemporal relationship between changes in Pi and forcewith Pi rising rapidly at the start of the contraction whenforce is well maintained and increasing only marginallylate in the contraction when force is falling rapidly (seeAllen & Westerblad, 2001, for discussion).

    Causes of slow relaxation

    The causes of the slow relaxation can, broadly, be eithera slow removal of activating calcium or a change incross bridge kinetics, possibly a slowing of cross bridgedetachment, as suggested by Edwards et al. (1975).Evidence to support the idea that cross bridge functionis altered as a result of high intensity metabolicallydemanding exercise first came from observations of theforcevelocity relationship of rat gastrocnemius muscle

    (de Haan et al. 1989) where the slowing of relaxation wasfound to be accompanied by a reduction in shorteningvelocity and a considerable loss of power. What was truefor rat gastrocnemius muscle was subsequently shownto be true for human muscle in situ with experimentson the adductor pollicis muscle (de Ruiter et al. 1999a;Fig. 4) fatigued under ischaemic conditions with repeatedtetanic contractions. While these findings clearly showthat there are changes in cross bridge function they donot actually explain the slow relaxation or rule out aslowing of calcium re-accumulation into the sarcoplasmicreticulum.However, direct observation of the intracellularfree calcium in mouse muscle fibres at room temperatureduring slow relaxation showed only small changes incalcium reuptake in the fatigued muscle fibres, the effectsof which were offset by a decrease in the affinity of theactin filaments for calcium (Westerblad & Allen, 1993).

    A further feature of fatigued muscle is that it becomesmore resistant to stretch. Figure 5 shows how fatigueleads to lower force when the muscle is allowed toshorten but when it is stretched the fatigued muscle offersmore resistance and this behaviour may explain the slowrelaxation from an isometric contraction. Relaxation froman isometric contraction in a singlefibre is characterisedbyan initial relatively slow linear phase of force decline, then

    Figure 3. Records of tension and [Ca2+]i from a single mouse muscle fibre (flexor brevis) during afatiguing runA shows the continuous tension record where each tetanus appears as a vertical line. Arrows indicate times whenthe intervals between tetani were changed. B shows [Ca2+]i and tension of tetani produced at times (a, b, c, d)indicated above the continuous tension record (from Westerblad & Allen, 1993).

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • 2980 D. A. Jones J Physiol 588.16

    Angular velocity (degrees/s)

    Fresh

    Fatigued

    0 100 200 300 400 500 600 700 800

    Pow

    er

    (%)

    Forc

    e (N

    )100

    908070605040302010

    0

    Figure 4. Forcevelocity relationships of fresh andfatigued human adductor pollicis muscle, togetherwith powerForce is given in absolute units (fresh, square symbols;fatigued, circles) while power is expressed as apercentage of the peak power of the fresh muscle(fresh, dashed line; fatigued continuous line) (from deRuiter et al. 1999a).

    a shoulder followed by a more rapid exponential decayof force. The shoulder, and subsequent loss of force, isassociated with relative movements of different segmentsof the fibre, generally with the ends being stretched(Huxley & Simmons, 1970). Curtin & Edman (1989)showed that these differential movements are reduced inthe fatigued state and are associated with an increasedresistance of the fibre to stretch which may act to stabilisethe fibre and prolong the relaxation phase (Curtin &Edman, 1994). Human muscle working in situ does notshow the two phases of relaxation but it does becomemore resistant to stretch. The shift in the forcevelocityrelationship (Fig. 5) shows how a fatigued muscle maybecome more stable and sustain force for longer once

    Figure 5. Forcevelocity relationships for fresh and fatiguedhuman adductor pollicis muscle both for shortening andlengthening contractionsFresh muscle, square symbols; fatigued muscle, circles. Data forshortening contractions, open symbols; during lengthening, filledsymbols. The vertical dotted line indicates the isometric condition towhich the data were normalised (from de Ruiter et al. 2000).

    stimulation stops since segments that begin to shortenand stretch other regions will develop less force, whilethose that are initially lengthened will be more resistant tostretch than would be the case for a fresh muscle.

    Loss of power with fatigue

    The data in Fig. 4 draw attention to the fact that whilethere may be relatively modest decrements in both forceand maximum velocity of unloaded shortening (Vmax) ofbetween 20 and 30%, when combined to generate power,the loss is considerable, reducing peak power to aboutone-third of the fresh value, largely explaining the oftendramatic and painful slowing seen as runners struggle tomaintain their speed in thehomestraightof a 400msprint,or the rapid loss of power in a standard Wingate test.

    What was not commented on at the time of theexperiments illustrated in Fig. 4 is that the shape ofthe forcevelocity relationship changes with fatigue,becoming more concave with a lower value of a/Po, asspecified in the Hill (1938) equation. The more concavethe relationship the less force is exerted at intermediatevelocities of shortening thereby reducing the peak power.The curvature also determines the force or velocity atwhich the maximum power is generated setting, forinstance, the cadence at which professional cyclists aimto ride and, as the curvature increases with fatigue, theoptimum velocity decreases. A subsequent examination ofthe factors determining power during a fatiguing series ofcontractions and recovery (Jones et al.2006; Fig. 6) showedthat the decrease in Vmax (Fig. 6C), which had been thefocus in earlier work, made the smallest contribution tothe loss of power (about 20%) while loss of force (Fig. 6B)and increased curvature (Fig. 6D) both contributed about40%. The contribution that changes in curvature make tothe loss of function with fatigue raises a number of inter-esting questions about the aspects of cross bridge inter-action that determine curvature and what may induce a

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • J Physiol 588.16 Changes in the forcevelocity relationship of muscle with fatigue 2981

    change in fatigued muscle. The fact that loss of power andchange in curvature are closely related to the slowing ofrelaxation initially suggested that the underlying changein cross bridge kinetics might be a slowing of crossbridge detachment (Edwards et al. 1975) and this wasthe hypothesis underlying much of our subsequent workon slowing and fatigue.

    Cross bridge mechanisms and possible changesin kinetics with fatigue

    In the Huxley (1957) model of cross bridge function thecurvature of the forcevelocity relationship is given bythe ratio (f+ g1)/g2, where f is the rate constant forattachment, g1 that for detachment in the region wherecross bridges develop active force, and g2 the rate constantfor detachment of negatively strained cross bridges. Theconstant g2 determines Vmax and the ratio (f + g1)/g2is the equivalent of a/Po in the Hill equation. In theexperiment shown in Fig. 6D, a/Po fell from 0.22 to0.11 with fatigue. To achieve this change in the ratio

    (f + g1)/g2, either g2 would have to double or the sumof the rate constants (f + g1) would need to halve. Infact Vmax, and thus g2, fell by about 20% so it is (f+ g1)that must have changed and would have had to decreaseto less than half the fresh value. The rate constant f isgenerally thought to be several times higher than g1 toensure a reasonably high proportion of attached crossbridges during an isometric contraction. In this case it isimpossible tomakemuch change in the ratio (f+ g1)/g2 byjust changing g1, the conclusion being that, contrary to theoriginal hypothesis, the slowing of cross bridge functionmust involve a substantial decrease in f , the rate constantfor attachment (Jones et al. 2006).

    The proposition that it is the rate of attachment ratherthan the rate of detachment which changes with fatiguecan be tested by measuring the economy of the muscle;more precisely, what is tested is whether the rate ofdetachment, g1, changes. The economy of a muscle is therate of energy utilisation per unit of force in the isometricstate. In a two-state model where cross bridges are eitherdetached and not generating force, or are attached and

    0

    20

    40

    60

    80

    100

    120

    0

    20

    40

    60

    80

    100

    120

    0

    20

    40

    60

    80

    100

    120

    0

    20

    40

    60

    80

    100

    120

    V max

    % in

    itial v

    alu

    e

    VmaxCurvature

    (a/Po)

    a/P o

    %

    initia

    l valu

    e

    0 50 100 150 200 250Time (s)

    300 350 400 450 5000 50 100 150 200 250Time (s)

    300 350 400 450 500

    0 50 100 150 200 250Time (s)

    300 350 400 450 5000 50 100 150 200 250Time (s)

    300 350 400 450 500

    Pow

    er

    % in

    itial v

    alu

    e

    Peak power

    F o %

    initia

    l valu

    e

    Isometric force

    A B

    C D

    Figure 6. Changes in contractile function during fatigue and recoveryHuman adductor pollicis fatigued with a series of ischaemic contractions and then allowed to recover. A, changesin peak power; B, isometric force; C, maximum velocity of unloaded shortening (Vmax); D, curvature of theforcevelocity relationship (a/Po). In each case the values are expressed as a percentage of those of the freshmuscle, also indicated by the dotted horizontal line (from Jones et al. 2006).

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • 2982 D. A. Jones J Physiol 588.16

    Conc

    entra

    tion

    (mM)

    0

    5

    10

    15

    20

    25

    30

    35A B

    0 4 8 12 16 20 24 28 32 0 4 8 12 16Time (s) Time (s)

    20 24 28 32

    PCPi

    ATP

    LA

    20

    40

    60

    80

    100

    120

    Forc

    e (%

    P o)

    Figure 7. Changes in muscle metabolites and isometric force with fatigueHuman anterior tibialis muscle fatigued by a series of tetani under ischaemic conditions. A, muscle metaboliteconcentrations estimated by magnetic resonance spectroscopy. PC, phosphocreatine; Pi, inorganic phosphate; LA,lactate, estimated from changes in pH and likely values of muscle buffering capacity. B, changes in isometric force(from Jones et al. 2009).

    generating force, the proportion of available cross bridgesthat are attached in the isometric state is given by the ratiof /(f + g1). Assuming that one ATP is used per cycle, asis likely to be the case in the isometric state or duringslow shortening (e.g. Piazzesi & Lombardi, 1995), thenthe ATP turnover is g1 times the number of attachedcross bridges i.e. g1fn/(f+ g1), where n is the numberof available cross bridges. Assuming that force per crossbridge remains constant, the total force is proportionalto the number of attached cross bridges, fn/(f+ g1), soif ATP turnover is divided by force to give the economyof the muscle this is proportional to g1 alone, the rateconstant for detachment. Dawson et al. (1980) found nochange in the economy of frog muscle as it fatigued and,likewise, Hultman & Sjostrom (1983) found no changein a biopsy study of human muscle. These findings havebeen confirmed more recently by a study using magnetic

    resonance spectroscopy (MRS) of the human anteriortibialis and, again, no change in economy was observedeven though the muscle became appreciably slower as itfatigued (Jones et al. 2009). The metabolite changes inthe muscle are shown in Fig. 7A and the isometric forcesustained in Fig. 7B, while in Fig. 8A the ATP turnover hasbeencalculated.The economy(Fig. 8B) remainedconstantthroughout the duration of the contraction. Althoughpower output and the forcevelocity relationship werenot measured in this experiment the close relationshipbetween slowing of relaxation and increased curvature(Jones et al. 2006) shows that relaxation is a good indicatorof changes in the forcevelocity relationship. The inferencefrom this, and previous studies measuring economy, isthat it is the rate constant for attachment, f , rather thang1, which decreases with fatigue, giving rise to the changein curvature and being amajor factor in the loss of power.

    0

    0.5

    1

    1.5

    2

    2.5

    3

    ATP

    turn

    over

    (mM

    s-1)

    0 5 10 15 20 25 30Time (s)

    0

    0.5

    1

    1.5

    2

    2.5

    3

    3.5

    4

    0 5 10 15Time (s)

    20 25 30

    ATP

    turn

    over

    (mM

    s-1)

    norm

    alis

    ed to

    initia

    l forc

    e

    A B

    Figure 8. ATP turnover and economy during a series of fatiguing contractionsA, ATP turnover derived from the data in Fig. 7A. B, economy of the muscle calculated as turnover in Fig. 8Adivided by the force in Fig. 7B. The data have been normalized to the value of the fresh muscle (from Jones et al.2009).

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • J Physiol 588.16 Changes in the forcevelocity relationship of muscle with fatigue 2983

    The rate constant for attachment

    In the two-state model of cross bridge action all theattached cross bridges exert force and the Huxley rateconstant f determines the rate of both attachment andthe generation of force. However, in reality there maybe a number of intermediate cross bridge states betweenthe attachment of myosin to actin and generation offorce (e.g. Regnier et al. 1995) and the rate constant fmust encompass all the individual steps. The changesin the forcevelocity relationship with fatigue, both forshortening and stretching as shown in Fig. 5, are verysimilar to the differences seen between fast and slow fibres(Linari et al. 2003). While slow fibres have lower Vmaxand greater curvature of the forcevelocity relationshipthan fast fibres during shortening, they sustain greaterforces during lengthening. The force sustained by theslow fibres was greater than that for the fast fibres whenexpressed relative to isometric although the absoluteforces were very similar. To explain this behaviour, Linariet al. concluded that during stretch of slow fibres thereis a greater recruitment of new force-generating crossbridges. These additional cross bridges could either be newattachments or cross bridges that were already attachedbut in a low force state where they do not contributeto the instantaneous stiffness of the fibre. The rapiditywith which the new force-generating cross bridges wererecruited at the start of a steady stretch argues in favour ofthe latter mechanism (Linari et al. 2003). It is an attractiveidea, therefore, that fatigue may result in a redistributionof cross bridges with a greater proportion in the low forcestate. Consequently the next question is what metabolicchange can cause an accumulation of low force crossbridges?

    Muscle metabolites and fatigue

    The metabolic changes in fatiguing muscle are shownin Fig. 7A and there are clearly a number of possiblecandidates that may affect force or the speed ofcontraction. Acidosis is often blamed for muscle fatigueand apart from an initial alkalosis as phosphocreatine isbroken down, the relationship shown in Fig. 8A mightsuggest this is, indeed, the case. However, there is ampleevidence now that pH changes play a relatively small partin the fatigue of mammalian muscle at normal physio-logical temperatures (see Allen et al. 2008). A directdemonstration that acidosis is not required for fatiguecomes from Cady et al. (1989) who found that a patientwith McArdles disease, who produced no H+ in hermuscle during contraction, still showed the characteristicloss of force and slow relaxation.

    Accumulation of ADP has been suggested to slowVmax (Westerblad et al. 1998) and ADP release fromthe bound cross bridge is generally regarded as the rate

    limiting step in the full cross bridge cycle (Nyitrail et al.2006). Although it cannot be measured directly by MRS,ADP concentrations can be estimated from the observedchanges in phosphocreatine, ATP and H+. However,the changes in concentration bear little or no temporalrelationship to the slowing of the muscle (Fig. 9C). Thedifficulty with ADP playing a major role is that myokinaseand AMP deaminase are very active enzymes in muscleand it is unlikely that ADP will remain at a high levelfor any length of time. Westerblad et al. (1998) foundthat in the fatigued state the velocity of shortening wasslower immediately after a longer tetanus compared toa short contraction, which they ascribed to a transientADP accumulation. There was then a partial recoveryin a matter of a few seconds, presumably as the ADPwas removed by enzyme action or diffusion. In the typeof experiment discussed here in which the muscles arefatigued whilst ischaemic, the slowing is not a transientphenomenonbut remains until the blood returns and onlythen recovers over several minutes (Fig. 6D), much moreslowly than would be expected if ADP were the causeof the problem. It is also notable that patients sufferingfrom myoadenylate deficiency, in whom high levels ofADP would be expected during muscle activity, do notshow any obvious abnormalities in muscle function eitherat rest or when fatigued (de Ruiter et al. 1999b) andmusclefatigue in adenylate kinase-deficient mice is also reportedto be little different to that of the wild-type (Hancock et al.2005).

    There is considerable interest in the possibility thataccumulation of Pi may affect cross bridge function infatigue. The release of Pi from the A.M.ADP.Pi complex(where A.M. is actomyosin) is closely associated with thegeneration of force and is a reversible process. High levelsof Pi in skinned fibre preparations decrease force andchange the distribution of cross bridge states so there is agreater proportion in a low force state, much as discussedabove in relation to the differences between fast and slowfibres (see, for example, Coupland et al. 2001; Caremaniet al.2008).There are, however, anumberofproblemswithPi being amajor cause of fatigue by acting directly on crossbridges. The first is the observation, evident in Fig. 9B, thatthe changes in Pi do not correlate at all well with changes inrelaxation. The major change in Pi occurs relatively earlyin the contraction when phosphocreatine is being brokendown and the muscle is functioning fairly well, yet whenthe muscle begins to fail there is relatively little furtherchange in Pi concentration. The effects of Pi on force inskinned fibres are also very temperature dependent, beingappreciable at low temperature and minimal at highertemperatures which approach the physiological levels ofthe human experiments discussed here (e.g. Couplandet al. 2001). The third problem is that Pi appears to bemost effective in influencing cross bridge function in therange of about 010mM, but human muscle, even at rest,

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • 2984 D. A. Jones J Physiol 588.16

    has an appreciable concentration of Pi of 58mM (Fig. 7A)so theremay be little scope for further effects as themusclefatigues.

    There are many reasons why the metaboliteconcentration measured in biopsy samples or by MRSmay not reflect the concentrations of metabolites actuallyinteracting with the cross bridges. Theremay, for instance,be different concentrations in the various fibre types orcompartmentation within the fibre. Equally, there neednot necessarily be a linear relationship betweenmetaboliteconcentration and function. Nevertheless the lack of clearrelationships suggests it may be instructive to look at othermechanisms that could affect curvature.

    Calcium and cross bridge kinetics

    Cross bridge kinetics and the rate of shortening havetraditionally been thought to be independent of theactivating calcium, but this may not be the case. The sum(f+ g1) in the Huxley model is equivalent to the rate atwhich tension will redevelop following rapid shortening

    and re-stretch (ktr, Brenner, 1988) and is known to besensitive to the activating calcium concentration, withf decreasing at low calcium. Likewise, the velocity ofunloaded shortening is also known to be affected bythe level of activation (Moss, 1986; McDonald, 2000;Morris et al. 2003). The mechanism of the slowing atlow levels of activation was suggested by Moss to be dueto an accumulation of long-lasting cross bridges whichprovide an internal resistance slowing the maximum rateof shortening. However, McDonald (2000) and Morriset al. (2003) both concluded that slower recruitment ofhigh force cross bridges during shortening leads to lowerforce so that in isotonic contractions a reduction in speedis necessary to maintain the target force. In the Huxleyanalysis this slowing would be apparent as a reduction inthe rate constant g2. If, therefore, both f and g2 are affectedby calcium then it is possible that the slowing of Vmaxand the decrease in curvature could both be explained bya decline in activating calcium that occurs with fatigue(Fig. 3). Thus it is possible that a reduction of intracellularcalcium as a result of some metabolic event, such as theaccumulation of Pi in the sarcoplasmic reticulum, could

    0

    5

    10

    15

    20

    25

    0 5 10 15 20 25 30 35[Pi] (mM)

    Rela

    xatio

    n ra

    te (s-

    1 ) Pi

    0.00 0.10 0.20 0.300

    5

    10

    15

    20

    25

    [H+] (M)

    Rela

    xatio

    n ra

    te (s-

    1 ) H+

    0

    5

    10

    15

    20

    25

    0 20 40 60 80 100 120[ADP] (M)

    Re

    laxa

    tion

    ra

    te (s-

    1 ) ADP

    BA

    C

    Figure 9. The relationship between relaxation rate and muscle metabolite concentrations during aseries of fatiguing contractionsData from the experiment shown in Fig. 6. A, hydrogen ion concentration; B, inorganic phosphate (Pi); C, ADP(from Jones et al. 2009).

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • J Physiol 588.16 Changes in the forcevelocity relationship of muscle with fatigue 2985

    play a part in all three of the characteristic features offatigue that determine the power output of a muscle, thereduced isometric force, slowing of Vmax and change incurvature. The emphasis here is on the word could sincewith intact fibres Westerblad et al. (1998) tested the ideathat low calcium was responsible for a reduction in Vmaxby exposing the fibres to dantrolene which reduced forcebut had no effect on shortening velocity.

    Another caveat is that there is a marked slowing ofrelaxation during moderate fatigue of frog muscle fibresat 12C (Curtin & Edman, 1989) but, in contrast toresults shown in Figs 4 and 5, Curtin & Edman (1994)found a decrease in the curvature of the forcevelocityrelationship as a result of fatigue, with a/Po increasing byabout 30%. De Ruiter & de Haan (2000) likewise foundthat the forcevelocity relationship became less curvedwhen human muscle was fatigued at low temperaturesalthough Vmax decreased and the muscle relaxed moreslowly. The two components of the Huxley ratio thatdetermine curvature, (f+ g1) and g2, must have differenttemperature coefficients since curvature, and thus theratio of (f+ g1)/g2, changes nearly threefold in the range2237C (de Ruiter & de Haan, 2000). Consequently fand g2 may respond differently to the metabolic changesof fatigue at high and low temperatures.

    In summary, there are some things we can say withcertainty. Firstly, a loss of power is a major consequenceof muscle fatigue and that in mammalian muscle atnormal physiological temperatures this is due to changesin three properties of the muscle: a decrease in isometricforce, a slowing of Vmax and an increase in curvatureof the forcevelocity relationship, this latter factor beingappreciated only relatively recently. Secondly, fatiguedmuscles are more resistant to stretch which suggests theremay be an increase in the proportion of cross bridgesin a state from which they can be rapidly recruited togenerate force. Metabolic causes for these changes arehard to identify and it is speculated that a decrease inactivating calcium might affect force, curvature and Vmaxand, consequently, make a contribution to all three of thechanges giving rise to the loss of power with fatigue.

    References

    Allen DG, Lamb GD & Westerblad H (2008). Skeletal musclefatigue: cellular mechanisms. Physiol Rev 88, 287332.

    Allen DG & Westerblad H (2001). Role of phosphate andcalcium stores in muscle fatigue. J Physiol 536, 657665.

    Brenner B (1988). Effect of Ca2+ on cross-bridge turnoverkinetics in skinned single rabbit psoas fibres: Implicationsfor regulation of muscle contraction. Proc Natl Acad SciU S A 85, 32653269.

    Cady EB, Elshove H, Jones DA & Moll A (1989). The metaboliccauses of slow relaxation in fatigued human skeletal muscle.J Physiol 418, 327337.

    Caremani M, Dantzig J, Goldman YE, Lombardi V & Linari M(2008). Effect of phosphate on the force and number ofmyosin cross-bridges during isometric contraction ofpermeabilized muscle fibres from rabbit psoas. Biophys J 95,57895808.

    Coupland ME, Puchert E & Ranatunga KW (2001).Temperature dependence of active tension in mammalian(rabbit psoas) muscle fibres: effect of inorganic phosphate.J Physiol 536, 879891.

    Curtin NA & Edman KA (1989). Effects of fatigue and reducedintracellular pH on segment dynamics in isometricrelaxation of frog muscle fibres. J Physiol 413, 159174.

    Curtin NA & Edman KA (1994). Forcevelocity relation forfrog muscle fibres: effects of moderate fatigue andintracellular acidification. J Physiol 475, 483494.

    Dawson MJ, Gadian DG & Wilkie DG (1980). Mechanicalrelaxation rate and metabolism studies in fatiguing muscleby phosphorous nuclear magnetic resonance. J Physiol 299,465484.

    De Haan A, Jones DA & Sargeant AJ (1989). Changes invelocity of shortening, power output and relaxation rateduring fatigue of rat medial gastrocnemius muscle. PflugersArch 413, 422428.

    De Ruiter CJ & De Haan A (2000). Temperature effect on theforce/velocity relationship of the fresh and fatigued humanadductor pollicis muscle. Pflugers Arch 440, 163170.

    De Ruiter CJ, Didden WJM, Jones DA & De Haan A (2000).The forcevelocity relationship of human adductor pollicismuscle during stretch and the effects of fatigue. J Physiol 526,671681.

    De Ruiter CJ, Jones DA, Sargeant AJ & De Haan A (1999a). Themeasurement of forcevelocity relationships of fresh andfatigued human adductor pollicis muscle. Eur J Appl Physiol80, 386393.

    De Ruiter CJ, Wevers RA, Van Engelen BGM, Verdjik PWL &De Haan A (1999b). Muscle function in a patient withBrodys disease. Muscle Nerve 22, 704711.

    Edwards RHT (1981). Human muscle function and fatigue. InHuman Muscle Fatigue: Physiological Mechanisms. CibaFoundation Symposium 82, ed. Porter R & Whelan J, pp.118. Pitman Medical Press, London.

    Edwards RHT, Hill DK & Jones DA (1972). Effect of fatigue onthe time course of relaxation from isometric contractions ofskeletal muscle in man. J Physiol 227, 2627P.

    Edwards RHT, Hill DK & Jones DA (1975). Metabolic changesassociated with the slowing of relaxation in fatigued mousemuscle. J Physiol 251, 287301.

    Hancock CR, Janssen E & Terjung RL (2005). Skeletal musclecontractile performance and ADP accumulation in adenylatekinase-deficient mice. Am J Physiol Cell Physiol 288,C1287C1297.

    Hill AV (1938). The heat of shortening and the dynamicconstants of muscle. Proc R Soc Lond B Biol Sci 126,136195.

    Hultman E & Sjostrom H (1983). Energy metabolism andcontraction force of human skeletal muscle in situ duringelectrical stimulation. J Physiol 345, 525532.

    Huxley AF & Simmons RM (1970). Rapid give and the tensionshoulder in the relaxation of frog muscle fibres. J Physiol210, 32P.

    C 2010 The Author. Journal compilation C 2010 The Physiological Society

  • 2986 D. A. Jones J Physiol 588.16

    Huxley AF (1957). Muscle structure and theories ofcontraction. Prog Biophys Biophys Chem 7, 255318.

    Jones DA, de Ruiter CJ & de Haan, A (2006). Change incontractile properties of human muscle in relationship to theloss of power and slowing of relaxation seen with fatigue.J Physiol 576, 913922.

    Jones DA, Turner DL, McIntyre DB & Newham DJ (2009).Energy turnover in relation to slowing of contractileproperties during fatiguing contractions of the humananterior tibialis muscle. J Physiol 587, 43294338.

    Linari M, Bottinelli R, Pellegrino MA, Reconditi M, Reggiani C& Lombardi V (2003). The mechanisms of the force responseto stretch in human skinned muscle fibres with differentmyosin isoforms. J Physiol 554, 335352.

    McDonald KS (2000). Ca2+ dependence of loaded shorteningin rat skinned cardiac myocytes and skeletal muscle fibres.J Physiol 525 169181.

    Morris CA, Tobacman LS & Homsher E (2003). Thin filamentactivation and unloaded shortening velocity of rabbitskinned muscle fibres. J Physiol 550, 205215.

    Moss RL (1986). Effects on shortening velocity of rabbitskeletal muscle due to variations in the level of thin-filamentactivation. J Physiol 377, 487505.

    Nyitrai1 M, Rossi R, Adamek N, Pellegrino MA, Bottinelli R &Geeves MA (2006). What limits the velocity of fast-skeletalmuscle contraction in mammals? J Mol Biol 355, 432442.

    Piazzesi G & Lombardi V (1995). A cross bridge model that isable to explain mechanical and energetic properties ofshortening muscle. Biophys J 68, 19661979.

    Regnier M, Morris C & Homsher E (1995). Regulation ofcross-bridge transition from a weakly to strongly bound statein skinned rabbit skeletal muscle fibers. Am J Physiol 269,C1532C1539.

    Westerblad H & Allen DG (1993). The contribution of [Ca2+]ito the slowing of relaxation in fatigued single fibres frommouse skeletal muscle. J Physiol 468, 729740.

    Westerblad H, Dahlstedt AJ & Lannergren J (1998).Mechanisms underlying reduced maximum shorteningvelocity during fatigue of intact, single fibres of mousemuscle. J Physiol 510, 269277.

    Acknowledgements

    Much of the work described here was carried out with Arnold deHaan and Jo de Ruiter in Amsterdam and with Tony Sargeant,Hans Degens and Sally Gilliver at Manchester MetropolitanUniversity. I owe a debt of gratitude to David Hill who firstintroduced me to the world of muscle physiology but most ofall I must acknowledge the kindness and support of RichardEdwards who had a major influence on my life and career.

    C 2010 The Author. Journal compilation C 2010 The Physiological Society